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When working with files in R, there are two ways to specify paths: 1. Using absolute paths (i.e. starting with C:/ or / on Windows and Mac/Lunix, respectively), or relative paths (possibly without any directory information). When working with the latter, where R looks will be based upon the working directory. You can get the working directory with getwd() and set the working directory with setwd(). In RStudio, you can also set the working directory on the Files tab by clicking More, then Set as Working Directory.

1. Chris Martin https://youtu.be/boZYP1mFUDw

We will use the lego R package in this class which contains information about every Lego set manufactured from 1970 to 2014, a total of 5710 sets.

devtools::install_github("seankross/lego")

library(lego)
data(legosets)

• Numerical (quantitative)
  • Continuous
  • Discrete
• Categorical (qualitative)
  • Regular categorical
  • Ordinal

str(legosets)

## Classes 'tbl_df', 'tbl' and 'data.frame':    6172 obs. of  14 variables:
##  $ Item_Number : chr  "10246" "10247" "10248" "10249" ...
##  $ Name        : chr  "Detective's Office" "Ferris Wheel" "Ferrari F40" "Toy Shop" ...
##  $ Year        : int  2015 2015 2015 2015 2015 2015 2015 2015 2015 2015 ...
##  $ Theme       : chr  "Advanced Models" "Advanced Models" "Advanced Models" "Advanced Models" ...
##  $ Subtheme    : chr  "Modular Buildings" "Fairground" "Vehicles" "Winter Village" ...
##  $ Pieces      : int  2262 2464 1158 898 13 39 32 105 13 11 ...
##  $ Minifigures : int  6 10 NA NA 1 2 2 3 2 2 ...
##  $ Image_URL   : chr  "http://images.brickset.com/sets/images/10246-1.jpg" "http://images.brickset.com/sets/images/10247-1.jpg" "http://images.brickset.com/sets/images/10248-1.jpg" "http://images.brickset.com/sets/images/10249-1.jpg" ...
##  $ GBP_MSRP    : num  132.99 149.99 69.99 59.99 9.99 ...
##  $ USD_MSRP    : num  159.99 199.99 99.99 79.99 9.99 ...
##  $ CAD_MSRP    : num  200 230 120 NA 13 ...
##  $ EUR_MSRP    : num  149.99 179.99 89.99 69.99 9.99 ...
##  $ Packaging   : chr  "Box" "Box" "Box" "Box" ...
##  $ Availability: chr  "Retail - limited" "Retail - limited" "LEGO exclusive" "LEGO exclusive" ...

Descriptive statistics:

• Contingency Tables
• Proportional Tables

Plot types:

• Bar plot
• Mosaic plot

table(legosets$Availability, useNA='ifany')

## 
##        LEGO exclusive    LEGOLAND exclusive         Not specified 
##                   695                     2                  1795 
##           Promotional Promotional (Airline)                Retail 
##                   141                    12                  3120 
##      Retail - limited               Unknown 
##                   403                     4

table(legosets$Availability, legosets$Packaging, useNA='ifany')

##                        
##                         Blister pack  Box Box with backing card Bucket
##   LEGO exclusive                  45  147                     0      1
##   LEGOLAND exclusive               0    2                     0      0
##   Not specified                    0   20                     0      0
##   Promotional                      0   44                     0      0
##   Promotional (Airline)            0   11                     0      0
##   Retail                          53 2575                    16     30
##   Retail - limited                 2  302                     1      5
##   Unknown                          0    1                     0      0
##                        
##                         Canister Foil pack Loose Parts Not specified Other
##   LEGO exclusive               0         0          71             7     5
##   LEGOLAND exclusive           0         0           0             0     0
##   Not specified                0         5           0          1739     0
##   Promotional                  0         0           1             0     3
##   Promotional (Airline)        0         0           0             1     0
##   Retail                      78       285           0             0    28
##   Retail - limited             0         1           0             0     0
##   Unknown                      0         0           0             0     0
##                        
##                         Plastic box Polybag Shrink-wrapped  Tag  Tub
##   LEGO exclusive                  1     412              0    6    0
##   LEGOLAND exclusive              0       0              0    0    0
##   Not specified                   6      24              0    0    1
##   Promotional                     2      90              0    0    1
##   Promotional (Airline)           0       0              0    0    0
##   Retail                          0       4             18    0   33
##   Retail - limited                1      86              0    0    5
##   Unknown                         0       3              0    0    0

library(vcd)
mosaic(HairEyeColor, shade=TRUE, legend=TRUE)

Descriptive statistics:

• Mean
• Median
• Quartiles
• Variance: \({ s }^{ 2 }=\sum _{ i=1 }^{ n }{ \frac { { \left( { x }_{ i }-\bar { x } \right) }^{ 2 } }{ n-1 } }\)
• Standard deviation: \(s=\sqrt{s^2}\)

Plot types:

• Dot plots
• Histograms
• Density plots
• Box plots
• Scatterplots

mean(legosets$Pieces, na.rm=TRUE)

## [1] 215.1686

median(legosets$Pieces, na.rm=TRUE)

## [1] 82

summary(legosets$Pieces)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##     0.0    30.0    82.0   215.2   256.2  5922.0     112

library(psych)
describe(legosets$Pieces, skew=FALSE)

##   vars    n   mean    sd median trimmed    mad min  max range   se
## 1    1 6060 215.17 356.2     82  140.29 103.78   0 5922  5922 4.58

describeBy(legosets$Pieces, group = legosets$Availability, skew=FALSE, mat=TRUE)

##    item                group1 vars    n      mean        sd median
## 11    1        LEGO exclusive    1  659 172.74203 442.96954   42.0
## 12    2    LEGOLAND exclusive    1    2 211.00000 154.14928  211.0
## 13    3         Not specified    1 1747 145.87178 309.19929   44.0
## 14    4           Promotional    1  140  53.97143 108.42721   28.0
## 15    5 Promotional (Airline)    1   12 126.16667  47.01612  127.0
## 16    6                Retail    1 3094 245.78119 294.78052  137.0
## 17    7      Retail - limited    1  402 410.94030 652.06435  207.5
## 18    8               Unknown    1    4  27.50000  15.96872   30.0
##      trimmed      mad min  max range         se
## 11  59.03403  40.0302   1 3428  3427  17.255643
## 12 211.00000 161.6034 102  320   218 109.000000
## 13  77.94210  53.3736   1 5195  5194   7.397620
## 14  31.96429  19.2738   1 1000   999   9.163772
## 15 130.10000  22.9803  10  203   193  13.572384
## 16 189.86470 153.4491   0 3803  3803   5.299546
## 17 260.56211 241.6638   1 5922  5921  32.522014
## 18  27.50000  12.6021   6   44    38   7.984360

Median and IQR are more robust to skewness and outliers than mean and SD. Therefore,

• for skewed distributions it is often more helpful to use median and IQR to describe the center and spread
• for symmetric distributions it is often more helpful to use the mean and SD to describe the center and spread

legosets[which(legosets$USD_MSRP >= 400),]

##      Item_Number                                   Name Year        Theme
## 901      2000430             Identity and Landscape Kit 2013 Serious Play
## 902      2000431                        Connections Kit 2013 Serious Play
## 2050     2000409                 Window Exploration Bag 2010 Serious Play
## 2852       10179 Ultimate Collector's Millennium Falcon 2007    Star Wars
##                       Subtheme Pieces Minifigures
## 901                                NA           6
## 902                              2455          NA
## 2050                             4900          NA
## 2852 Ultimate Collector Series   5195           5
##                                                 Image_URL GBP_MSRP
## 901  http://images.brickset.com/sets/images/2000430-1.jpg   509.99
## 902  http://images.brickset.com/sets/images/2000431-1.jpg   490.18
## 2050 http://images.brickset.com/sets/images/2000409-1.jpg   314.99
## 2852   http://images.brickset.com/sets/images/10179-1.jpg   342.49
##      USD_MSRP CAD_MSRP EUR_MSRP     Packaging  Availability
## 901    789.99   789.99   699.99 Not specified Not specified
## 902    754.99   754.99   559.99 Not specified Not specified
## 2050   484.99   484.99   359.99 Not specified Not specified
## 2852   499.99       NA       NA Not specified Not specified

legosets[which(legosets$Pieces >= 4000),]

##      Item_Number                                   Name Year
## 2047       10214                           Tower Bridge 2010
## 2050     2000409                 Window Exploration Bag 2010
## 2628       10189                              Taj Mahal 2008
## 2852       10179 Ultimate Collector's Millennium Falcon 2007
##                Theme                  Subtheme Pieces Minifigures
## 2047 Advanced Models                 Buildings   4287          NA
## 2050    Serious Play                             4900          NA
## 2628 Advanced Models                 Buildings   5922          NA
## 2852       Star Wars Ultimate Collector Series   5195           5
##                                                 Image_URL GBP_MSRP
## 2047   http://images.brickset.com/sets/images/10214-1.jpg   209.99
## 2050 http://images.brickset.com/sets/images/2000409-1.jpg   314.99
## 2628   http://images.brickset.com/sets/images/10189-1.jpg   199.99
## 2852   http://images.brickset.com/sets/images/10179-1.jpg   342.49
##      USD_MSRP CAD_MSRP EUR_MSRP     Packaging     Availability
## 2047   239.99   299.99   219.99           Box Retail - limited
## 2050   484.99   484.99   359.99 Not specified    Not specified
## 2628   299.99   399.99       NA           Box Retail - limited
## 2852   499.99       NA       NA Not specified    Not specified

Likert scales are a type of questionaire where respondents are asked to rate items on scales usually ranging from four to seven levels (e.g. strongly disagree to strongly agree).

library(likert)
library(reshape)
data(pisaitems)
items24 <- pisaitems[,substr(names(pisaitems), 1,5) == 'ST24Q']
items24 <- rename(items24, c(
            ST24Q01="I read only if I have to.",
            ST24Q02="Reading is one of my favorite hobbies.",
            ST24Q03="I like talking about books with other people.",
            ST24Q04="I find it hard to finish books.",
            ST24Q05="I feel happy if I receive a book as a present.",
            ST24Q06="For me, reading is a waste of time.",
            ST24Q07="I enjoy going to a bookstore or a library.",
            ST24Q08="I read only to get information that I need.",
            ST24Q09="I cannot sit still and read for more than a few minutes.",
            ST24Q10="I like to express my opinions about books I have read.",
            ST24Q11="I like to exchange books with my friends."))

l24 <- likert(items24)
summary(l24)

##                                                        Item      low
## 10   I like to express my opinions about books I have read. 41.07516
## 5            I feel happy if I receive a book as a present. 46.93475
## 8               I read only to get information that I need. 50.39874
## 7                I enjoy going to a bookstore or a library. 51.21231
## 3             I like talking about books with other people. 54.99129
## 11                I like to exchange books with my friends. 55.54115
## 2                    Reading is one of my favorite hobbies. 56.64470
## 1                                 I read only if I have to. 58.72868
## 4                           I find it hard to finish books. 65.35125
## 9  I cannot sit still and read for more than a few minutes. 76.24524
## 6                       For me, reading is a waste of time. 82.88729
##    neutral     high     mean        sd
## 10       0 58.92484 2.604913 0.9009968
## 5        0 53.06525 2.466751 0.9446590
## 8        0 49.60126 2.484616 0.9089688
## 7        0 48.78769 2.428508 0.9164136
## 3        0 45.00871 2.328049 0.9090326
## 11       0 44.45885 2.343193 0.9609234
## 2        0 43.35530 2.344530 0.9277495
## 1        0 41.27132 2.291811 0.9369023
## 4        0 34.64875 2.178299 0.8991628
## 9        0 23.75476 1.974736 0.8793028
## 6        0 17.11271 1.810093 0.8611554

There is only one pie chart in OpenIntro Statistics (Diez, Barr, & Çetinkaya-Rundel, 2015, p. 48). Consider the following three pie charts that represent the preference of five different colors. Is there a difference between the three pie charts? This is probably a difficult to answer.

There is only one pie chart in OpenIntro Statistics (Diez, Barr, & Çetinkaya-Rundel, 2015, p. 48). Consider the following three pie charts that represent the preference of five different colors. Is there a difference between the three pie charts? This is probably a difficult to answer.

Source: https://en.wikipedia.org/wiki/Pie_chart.

A census involves collecting data for the entire population of interest. This is problematic for several reasons, including:

• It can be difficult to complete a census: there always seem to be some individuals who are hard to locate or hard to measure. And these difficult-to-find people may have certain characteristics that distinguish them from the rest of the population.
• Populations rarely stand still. Even if you could take a census, the population changes constantly, so it’s never possible to get a perfect measure.
• Taking a census may be more complex than sampling.

Sampling involves measuring a subset of the population of interest, usually randomly.

• Non-response: If only a small fraction of the randomly sampled people choose to respond to a survey, the sample may no longer be representative of the population.
• Voluntary response: Occurs when the sample consists of people who volunteer to respond because they have strong opinions on the issue. Such a sample will also not be representative of the population.
• Convenience sample: Individuals who are easily accessible are more likely to be included in the sample.

• Observational study: Researchers collect data in a way that does not directly interfere with how the data arise, i.e. they merely “observe”, and can only establish an association between the explanatory and response variables.
• Experiment: Researchers randomly assign subjects to various treatments in order to establish causal connections between the explanatory and response variables.

Source: XKCD 552 http://xkcd.com/552/

1. Control: Compare treatment of interest to a control group.
2. Randomize: Randomly assign subjects to treatments, and randomly sample from the population whenever possible.
3. Replicate: Within a study, replicate by collecting a sufficiently large sample. Or replicate the entire study.
4. Block: If there are variables that are known or suspected to affect the response variable, first group subjects into blocks based on these variables, and then randomize cases within each block to treatment groups.

Difference between blocking and explanatory variables

• Factors are conditions we can impose on the experimental units.
• Blocking variables are characteristics that the experimental units come with, that we would like to control for.
• Blocking is like stratifying, except used in experimental settings when randomly assigning, as opposed to when sampling.

• Placebo: fake treatment, often used as the control group for medical studies
• Placebo effect: experimental units showing improvement simply because they believe they are receiving a special treatment
• Blinding: when experimental units do not know whether they are in the control or treatment group
• Double-blind: when both the experimental units and the researchers who interact with the patients do not know who is in the control and who is in the treatment group

• ggplot2 is an R package that provides an alternative framework based upon Wilkinson’s (2005) Grammar of Graphics.
• ggplot2 is, in general, more flexible for creating "prettier" and complex plots.
• Works by creating layers of different types of objects/geometries (i.e. bars, points, lines, polygons, etc.) ggplot2 has at least three ways of creating plots:
  1. qplot
  2. ggplot(...) + geom_XXX(...) + ...
  3. ggplot(...) + layer(...)
• We will focus only on the second.

• Data
  ggplot(myDataFrame, aes(x=x, y=y)
• Layers
  geom_point(), geom_histogram()
• Facets
  facet_wrap(~ cut), facet_grid(~ cut)
• Scales
  scale_y_log10()
• Other options
  ggtitle('my title'), ylim(c(0, 10000)), xlab('x-axis label')

ls('package:ggplot2')[grep('geom_', ls('package:ggplot2'))]

##  [1] "geom_abline"          "geom_area"            "geom_bar"            
##  [4] "geom_bin2d"           "geom_blank"           "geom_boxplot"        
##  [7] "geom_contour"         "geom_count"           "geom_crossbar"       
## [10] "geom_curve"           "geom_density"         "geom_density_2d"     
## [13] "geom_density2d"       "geom_dotplot"         "geom_errorbar"       
## [16] "geom_errorbarh"       "geom_freqpoly"        "geom_hex"            
## [19] "geom_histogram"       "geom_hline"           "geom_jitter"         
## [22] "geom_label"           "geom_line"            "geom_linerange"      
## [25] "geom_map"             "geom_path"            "geom_point"          
## [28] "geom_pointrange"      "geom_polygon"         "geom_qq"             
## [31] "geom_quantile"        "geom_raster"          "geom_rect"           
## [34] "geom_ribbon"          "geom_rug"             "geom_segment"        
## [37] "geom_smooth"          "geom_spoke"           "geom_step"           
## [40] "geom_text"            "geom_tile"            "geom_violin"         
## [43] "geom_vline"           "update_geom_defaults"